Identifying Causal Effects using Instrumental Time Series: Nuisance IV and Correcting for the Past

Instrumental variable (IV) regression relies on instruments to infer causal effects from observational data with unobserved confounding. We consider IV regression in time series models, such as vector auto-regressive (VAR) processes. Direct applications of i.i.d. techniques are generally inconsistent as they do not correctly adjust for dependencies in the past. In this paper, we propose methodology for constructing identifying equations that can be used for consistently estimating causal effects. To do so, we develop nuisance IV, which can be of interest even in the i.i.d. case, as it generalizes existing IV methods. We further propose a graph marginalization framework that allows us to apply nuisance and other IV methods in a principled way to time series. Our framework builds on the global Markov property, which we prove holds for VAR processes. For VAR(1) processes, we prove identifiability conditions that relate to Jordan forms and are different from the well-known rank conditions in the i.i.d. case (they do not require as many instruments as covariates, for example). We provide methods, prove their consistency, and show how the inferred causal effect can be used for distribution generalization. Simulation experiments corroborate our theoretical results. We provide ready-to-use Python code.